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The paper proposes a new method of current measurement of the layer thickness of optical films in the process of their forming, in particular, by the method of vacuum deposition. Such films, among other things, are used to create a variety of optoelectronic devices and optical nanosensors for laboratory research in the chemical and pharmaceutical industries, for environmental monitoring. We propose a method for measuring the phase of a laser beam, which is based on heterodyne interferometry. The method of heterodyne interferometry in comparison with ordinary interference methods provides better S/N ration results due to the transfer of the investigated signal from the low frequency domain to heterodyne frequency. Our proposed approach is the three-wave heterodyne interferometry (TGI), otherwise - TWI (three waves interference). The TGI method is designed to critically increase the sensitivity to small amplitudes of laser Doppler vibrometers and increase their noise resistance. In interference gauges of optical film thickness, in refractometers, and in many other film thickness gauges as well as in laser Doppler vibrometers the investigated parameter is the phase shift of probing optical radiation. Therefore, the developments of TGI in laser Doppler vibrometers can be used to measure the phase shift. The analysis of the new method on mathematical model of TGI was provided. We have got the relations of the output signal of a three-wave heterodyne interferometer dependence on the phase shift , as well as on the thickness of optical films and on their refractive index. The simulation results show that for the optoelectronic equipment that provides with an error of up to 10 %, the absolute error of phase shift measurement, compared to the classical heterodyne interferometer, can be reduced to 103 times. The same results applies to the thickness of the optical coating layer. The paper also analyzes the results of experiments on the use of TGI in laser vibrometers and shows that they indicate the possibility of measuring the phase  of optical radiation up to 10-5. The disadvantage of the proposed method is its non-linearity and, as a result, a limited linear range. Ways of extending the linear range are discussed.

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The main purpose of this article is to prove the limit theorem for a singular spectral function A*m(aO of the random matrix A = s" 1 Σ?=ι Xi> where X,·, t = 1,*, are independent observations on the matrix A -f Ξ, where A = (a»j)> * = 1, TO, j = 1, m, is a real matrix and Ξ is a random matrix.These results are given under certain assumptions on Λ, Ξ, n, m, and s by means of the Stieltjes transform for the spectral functions of the matrix A'A.

Authors created and provided the operation of the first version of the "Bolide Network of Churyumov" for continuous recording of twilight and daytime traces of aerial and aerospace intrusions over Kiev and Kiev district during 2013-2016. A total of more than 36000 copyright photos was obtained, their classification was carried out and the first database was created. The authors recorded typical space invading meteoroids, comets nucleus fragments and traces of aerial intrusions, signs of which, as a rule, are observed at lower altitudes comparing with typical space invasions.